5(x+4)=3x(x+10)-8

Solution for 5(x+4)=3x(x+10)-8 equation:

5(x+4)=3x(x+10)-8

We move all terms to the left:

5(x+4)-(3x(x+10)-8)=0

We multiply parentheses

5x-(3x(x+10)-8)+20=0


We calculate terms in parentheses: -(3x(x+10)-8), so:

3x(x+10)-8

We multiply parentheses

3x^2+30x-8

Back to the equation:

-(3x^2+30x-8)


We get rid of parentheses

-3x^2+5x-30x+8+20=0

We add all the numbers together, and all the variables

-3x^2-25x+28=0

a = -3; b = -25; c = +28;
Δ = b2-4ac
Δ = -252-4·(-3)·28
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-31}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+31}{2*-3}=\frac{56}{-6}
=-9+1/3
$